Po Hu

Exact Global Modes of Two-Term Weighted Sums of i.i.d. Geometric Random Variables

Let X and Y be independent geometric random variables on Z≥0 with P(X = k) =P(Y = k) =p(1 − p)^k. For positive integers a, b, we determine the global modes of Z = aX + bY . The probability mass function may have gaps and local rises and falls. We prove that every global mode is a...

Exact Global Modes of Two-Term Weighted Sums of i.i.d. Geometric Random Variables

Let X and Y be independent geometric random variables on Z≥0 with P(X = k) =P(Y = k) =p(1 − p)^k. For positive integers a, b, we determine the global modes of Z = aX + bY . The probability mass function may have gaps and local rises and falls. We prove that every global mode is a...